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Title: A Note on plane rational curves and the associated Poncelet Surfaces
Authors: Bernardi, Alessandra
Gimigliano, Alessandro
Idà, Monica
Keywords: plane rational curves, Poncelet surfaces, singularities.
Issue Date: 2015
Publisher: EUT Edizioni Università di Trieste
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
47 (2015)
We consider the parametrization (f0, f1, f2) of plane
rational curve c, and we want to relate the splitting type of C (i.e.
the second Betti numbers of the ideal (f0, f1, f2) with the
singularities of the associated Poncelet surface in p3. We are able of doing this for Ascenzi curves, thus generalizing a result in [8] in the
case of plane curves. Moreover we prove that if the Poncelet surface
s C p3 is singular then it is associated with a curve C which possesses
at least a point of multiplicity >_ 3.
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/0049-4704/11219
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.47 (2015)

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